Question

A charge moves a distance of 15.0 cm in the direction of a uniform electric field whose magnitude is 195 N/C. As the charge moves, its electrical potential energy increases by 7.5 × 10−6 J. What is the charge on the moving particle?

Answer 1

By the definition, electrical potential energy is the energy that is needed to move a charge against an electric field. The change in electrical potential energy of the charge can be found as follows:

$$\Delta U=U_f-U_i=-W,$$ $$\Delta U=-W=-qEd,$$ $$q=-\dfrac{-\Delta U}{Ed}=-\dfrac{-7.5\cdot10^{-6}\ J}{195\ \dfrac{N}{C}\cdot 0.15\ m}=2.56\cdot10^{-7}\ C.$$

Answer:

$q=2.56\cdot10^{-7}\ C.$